# [time-nuts] Another "atomic" clock question

Lars Walenius lars.walenius at hotmail.com
Fri Mar 7 12:02:04 EST 2014

```As I am a poor programmer and also lazy (includes hardware and software), I would like to ask the following question: How much better would a GPSDO like the Arduino GPSDO be with added sawtooth correction?

Let’s say we assume the 1ns resolution TIC is perfect, no jitter from the uP and the DAC have a perfect frequency setting resolution of 1E-13. The receiver in my case is a M12 set in position hold mode after a survey and my measured ADEV starts at 2E-8 for 1sec and is 2E-11 at 1000secs. The MDEV is 2E-8 at 1sec and 2E-12 at 1000sec (very similar to what found on the leapsecond.com M12 page). The oscillator is my “8663”-type OCXO that I have measured to have an ADEV just above 1E-12 over the range 1-10000secs. Let’s say the oscillator is perfect at 2E-12 over 1-10000secs.

The Arduino GPSDO control loop works as follows, as far as I understand, if set to a time constant =1000secs and damping =2 :

TIC value is pre-filtered similar to an RC filter with 250seconds time constant (I like to refer to analog RC-filters being an RF and analog engineer)

The filtered TIC value is divided by the time constant 1000 and adjusts the DAC proportional to this.

The filtered TIC value integrates the DAC value after dividing it by (time constant * time constant * damping) = (/1000/1000/2).

My explicit question is how much better the ADEV of the GPSDO oscillator output will be with sawtooth correction added in the software? Another question is how much better the ADEV will be if the TIC had a resolution of 0.1nsec instead? Maybe a third question could be if the DAC only had 1E-12 resolution?

Is some more important factors needed to be known to calculate this to a reasonable accuracy? e.g. room temperature variations of the M12.

In my own measurements, with about the same conditions as above with a time constant of 1000s, I got an output ADEV of about 3E-12 at Tau 1000s measured with an HP5370 against an LPRO Rb (plot was attached to Arduino GPSDO thread Feb 12 2014). This value looks very similar to the combination of the 1PPS MDEV and OCXO ADEV. Is that just a coincidence?

Lars
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